Inner tracks vs outer tracks

Yes.  There are millions of words on this subject on this forum and on any other forum devoted to vinyl.  Too many, in fact.  Read any thread on cartridge alignment.  Try not to get crazy.

The Stevenson alignment was designed to minimize inner groove distortion.  Many/most classical recordings reach a crescendo at the end where this may be more important.

Yes. There should also be differences outside to inside due to tracking error. There should also be differences due to stylus drag changes as volume changes affecting anti-skate. Lets see now, if its a uni-pivot there should also be changes pretty much all the time due to everything. But if its a gimbal arm there should be changes due to bearing chatter. There should also be changes as the Earth turns on its axis and magma shifts affect local gravity. 

The true answer is because the record turns at constant RPM, but the circumference decreases as you go in, then the lower surface speed should result in lower bandwidth and lower sound quality.

As with all the other stuff though the operative word is "should". Let me know if it actually does.